1. Field of the Invention
The present invention relates generally to the field of photonic crystals; and, more particularly, to two-dimensional photonic crystal slab apparatus and to a method for fabricating a two-dimensional photonic crystal slab apparatus.
2. Description of the Prior Art
Photonic crystals (PC) are periodic dielectric structures which can prohibit the propagation of light in certain frequency ranges. More particularly, photonic crystals have spatially periodic variations in refractive index; and with a sufficiently high refractive index contrast, photonic bandgaps can be opened in the structure""s optical spectrum. (The term xe2x80x9cphotonic bandgapxe2x80x9d as used herein and as used in the art is a frequency range within which propagation of light through the photonic crystal is prevented. In addition, the term xe2x80x9clightxe2x80x9d as used herein is intended to include radiation throughout the electromagnetic spectrum, and is not limited to visible light.)
A photonic crystal that has spatial periodicity in three dimensions can prevent the propagation of light having a frequency within the crystal""s bandgap in all directions; however, fabrication of such a structure is technically challenging. A more attractive alternative is to utilize a two-dimensional photonic crystal slab that has a two-dimensional periodic lattice incorporated within it. In a structure of this sort, light propagating in the slab is confined in the direction perpendicular to a major surface of the slab via total internal reflection; whereas propagation in other directions is controlled by the properties of the photonic crystal slab. In addition to being easier to fabricate, two-dimensional photonic crystal slabs provide the further advantage that they are compatible with the planar technologies of standard semiconductor processing.
It is known that introducing defects in the periodic structure of a photonic crystal allows the existence of localized electromagnetic states that are trapped at the defect site, and that have resonant frequencies within the bandgap of the surrounding photonic crystal material. By providing a line of such defects extending through the photonic crystal, a waveguiding structure is created that can be used in the control and guiding of light (see J. D. Joannopoulos, R. D. Meade, and J. N. Winn, xe2x80x9cPhotonic Crystalsxe2x80x9d, Princeton University Press, Princeton, N.J., 1995).
A two-dimensional photonic crystal slab waveguide often comprises a two-dimensional periodic lattice in the form of an array of posts incorporated in a slab body. The posts can, for example, comprise holes in a slab body of dielectric material (see U.S. Pat. No. 6,134,369), or the posts can comprise dielectric rods and the slab body can be air, another gas or a vacuum. In addition, the posts can comprise rods of a dielectric material having a first refractive index and the slab body can comprise a dielectric material having a second refractive index different from the first refractive index. In any of these devices, the guided modes within the two-dimensional photonic crystal slab may suffer high losses due to the overlap of these modes with leaky modes. These leaky modes will eventually escape into the upper and/or lower cladding for the photonic crystal. High guiding efficiency can be achieved only in a narrow frequency region, close to the upper or lower edge (for dielectric rods or holes, respectively) of the waveguide band, where there are no leaky modes (see S. G. Johnson, S. Fan, P. R. Villeneuve, L. Kolodziejski and J. D. Joannopoulos, Phys. Rev. B 60, 5751, 1999 and S. G. Johnson, P. R. Villeneuve, S. Fan and J. D. Joannopoulos, Phys. Rev. B 62, 8212, 2000).
For both holes and the dielectric rod designs, there are also problems with the mixing between TE-like and TM-like waves. Since only one type of waves exhibits a full band gap, this mixing of the two types of waves can be expected to increase the losses. The mixing of the two modes can happen either by changing the polarization of the incident light or by breaking the mirror symmetry of the structure relative to the plane in the middle of the two-dimensional photonic crystal slab. Defects in the structure or an asymmetric cladding for the device (e.g., an air cladding on top and a low dielectric material cladding below) can easily break that symmetry. Using a Bragg mirror (or a one-dimensional photonic crystal) for cladding material is not going to help much because the photonic crystal will not have a complete photonic bandgap and there will still be a problem with leaky modes (see U.S. Pat. No. 6,134,043).
Also, for the design in which dielectric rods are provided within an air slab body, the height of the rods should be about two times the lattice constant. This makes the fabrication of these structures rather difficult.
Embodiments of the present invention provide two-dimensional photonic crystal slab apparatus and a method for fabricating a two-dimensional photonic crystal slab apparatus. A two-dimensional photonic crystal slab apparatus according to the invention may comprise a photonic crystal slab that includes a two-dimensional periodic lattice, and upper and lower cladding layers for the photonic crystal slab, the upper and lower cladding layers each including a metallic cladding layer.
According to a first embodiment of the invention, the two-dimensional photonic crystal slab apparatus comprises a two-dimensional photonic crystal slab waveguide apparatus in which the photonic crystal slab includes a waveguide that is capable of transmitting light having a frequency within a bandgap of the photonic crystal slab. Preferably, the waveguide is created by providing a region of defects in the two-dimensional periodic lattice of the slab. Specifically, the two-dimensional periodic lattice may comprise a two-dimensional array of dielectric structures, such as dielectric rods; and the region of defects may be provided by reducing the radii of a line of the rods or by omitting a line of the rods.
A two-dimensional photonic crystal slab waveguide apparatus according to an embodiment of the present invention achieves substantially perfect transmission of light through the waveguide, even along waveguides that are tightly bent. This is achieved, at least in part, because the upper and lower metallic cladding layers cause the light to be confined between the two metallic layers, such that there are no losses due to the coupling to leaky modes of the cladding layers.
In addition, it can be shown that TE-like modes can be moved to frequencies above the lowest bandgap of TM-like modes by changing the separation between the metallic layers. Thus, for a separation of 0.5a (a is the lattice constant), one can have a complete bandgap for the TM-like modes (see A. A. Maradudin and A. R. McGurn, J. Opt. Soc. Am., 10, 307, 1993). This facilitates fabrication of the waveguide apparatus since the rods forming the two-dimensional array can be made shorter.
According to another embodiment of the present invention, a method for fabricating a two-dimensional photonic crystal slab apparatus is provided. A method for fabricating a two-dimensional photonic crystal slab apparatus according to the invention may include providing a dielectric slab supported on a substrate, forming a two-dimensional array of dielectric structures in the dielectric slab to form a two-dimensional photonic crystal slab, and forming first and second cladding layers on first and second surfaces of the photonic crystal slab, the first and second cladding layers each including a metallic cladding layer.
According to an embodiment of the invention, forming a two-dimensional array of dielectric structures in the dielectric slab comprises forming a two-dimensional array of structures using an etch process. As is well-known, it is usually difficult to grow optical quality semiconductors on metals. The fabrication method according to the present invention does not require the growing of crystals; and, accordingly, is particularly suitable for use in fabricating two-dimensional photonic crystal slab apparatus having metallic cladding layers. Forming first and second cladding layers on first and second surfaces of the photonic crystal slab can be accomplished in various ways, depending on various kinds of materials used in fabricating the apparatus.
As is also known in the art, it is desirable that the two-dimensional photonic crystal slab be fabricated from single crystalline materials; and the fabrication method of the present invention permits various kinds of material systems to be utilized; including, for example, systems based on Si, InGaAsP and GaAs. In general, the fabrication method according to embodiments of the present invention can be utilized with any of these systems with only minor modification of the method being required.
Yet further advantages and specific details of the present invention will become apparent hereinafter in conjunction with the following detailed description of the invention.